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Example, 2 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at August 13, 2026 by Teachoo
Chapter 11 Class 12 Three Dimensional Geometry
Concept wise
-
Direction cosines and ratios
- Equation of line - given point and //vector
- Equation of line - given 2 points
- Angle between two lines - Vector
- Angle between two lines - Cartisian
- Angle between two lines - Direction ratios or cosines
- Shortest distance between two skew lines
- Shortest distance between two parallel lines
- Equation of plane - In Normal Form
- Equation of plane - Prependicular to Vector & Passing Through Point
- Equation of plane - Passing Through 3 Non Collinear Points
- Equation of plane - Intercept Form
- Equation of plane - Passing Through Intersection Of Planes
- Coplanarity of 2 lines
- Angle between two planes
- Distance of point from plane
- Angle between Line and Plane
- Equation of line under planes condition
- Point with Lines and Planes
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Transcript
Example 2 If a line has direction ratios 2, โ 1, โ 2, determine its direction cosines.If direction ratios of a line are a, b, c direction cosines are ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) , ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) , ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) Given, Direction ratios = 2, โ1, โ2 โด ๐ = 2, b = โ1, c = โ2 Also, โ(๐^๐ + ๐^๐ + ๐^๐ ) = โ(22 + (โ1)2 + (โ2)2) = โ(4 + 1 + 4) = โ9 = 3 Direction cosines = ๐/โ(๐^2 + ๐^2 + ๐^2 ) , ๐/โ(๐^2 + ๐^2 + ๐^2 ) , ๐/โ(๐^2 + ๐^2 + ๐^2 ) = ๐/๐ , (โ๐)/๐ , (โ๐)/๐
